Classi¯ers fusion for improved vessel recognition with application in quanti¯cation of generalized arteriolar narrowing

This paper attempts to estimate diagnostically relevant measure, i.e., Arteriovenous Ratio with an improved retinal vessel classi¯cation using feature ranking strategies and multiple classi¯ers decision-combination scheme. The features exploited for retinal vessel characterization are based on statistical measures of histogram, di®erent ¯lter responses of images and local gradient information. The feature selection process is based on two feature ranking approaches (Pearson Correlation Coe±cient technique and Relief-F method) to rank the features followed by use of maximum classi¯cation accuracy of three supervised classi¯ers ( k -Nearest Neighbor, Support Vector Machine and Na ï ve Bayes) as a threshold for feature subset selection. Retinal vessels are labeled using the selected feature subset and proposed hybrid classi¯cation scheme, i.e., decision fusion of multiple classi¯ers. The comparative analysis shows an increase in vessel classi¯cation accuracy as well as Arteriovenous Ratio calculation performance. The system is tested on three databases, a local dataset of 44 images and two publically available databases, INSPIRE-AVR containing 40 images and VICAVR containing 58 images. The local database also contains images with pathologically diseased structures. The performance of the proposed system is assessed by comparing the experimental results with the gold standard estimations as well as with the results of previous methodologies. Overall, an accuracy of 90.45%, 93.90% and 87.82% is achieved in retinal blood vessel separation with 0.0565, 0.0650 and 0.0849 mean error in Arte-riovenous Ratio calculation for Local, INSPIRE-AVR and VICAVR dataset, respectively.


Introduction
Cardiovascular diseases including coronary heart disease, stroke and hypertension are characterized by the deviations in blood vascular structure. 1,2 In hypertension, arteries are altered from the regular pattern and the inner lining of arteries is damaged and as a result, they become thick and sti®. 3 Due to this thickness of artery-walls in hypertension, the normal blood°ow pressure is a®ected. 4 Along with other body organs including heart and kidney, the presence of hypertension also a®ects eye and leads to several ocular disorders including Hypertensive Retinopathy (HR). 5 In HR, both the vascular and nonvascular structures in retina are deteriorated. However, the alteration of retinal vessel width is considered as an earliest biomarker of HR. 6 Particularly, the width of arteries is narrowed in initial stages, that is why \arteriolar narrowing" is placed at initial stage in all the three scales proposed so far for HR diagnosis. [7][8][9][10] For assessment of arteriolar narrowing, a parameter called Arteriovenous Ratio (AVR), suggested by Stokoe and Turner, 11 is used. It is the ratio of average diameter of retinal Arterioles (arteries) to average Venules (veins) diameter and its calculation involves the use of two other parameters known as Central Retinal Artery Equivalent and Central Retinal Venular Equivalent. 12,13 The deviation of this parameter from a normal range indicates the presence of HR so this biomarker is considered crucial for HR severity assessment. In order to quantify the AVR, the ophthalmologists examine the internal structure of retina using the photographs obtained via di®erent imaging modalities, i.e., Ophthalmoscopy, Fluorescein Angiography and Fundus Photography, however, fundus imaging is the only non-invasive imaging method that provides a mode for extensive visualization of blood vessels and other structures in retina. Moreover, according to the studies, [14][15][16] the fundus camera has the additional capability of improving retina visualization and consequently the detection of retinal diseases. Figure 1 illustrates a sample retinal fundus image taken from local database with several anomalies that occur in HR.
Generally, AVR is manually estimated by ophthalmologists through visual screening of retina in fundus image which is a time-taking and laborintensive process. The ophthalmologist¯rst manually performs vessel classi¯cation in retinal photographs and then estimates AVR. To assist the ophthalmologist to speed up the detection process, the digital image processing techniques and computer vision tools are being used for e±cient and timely diagnosis of HR. [17][18][19][20][21][22] Automated HR detection systems generally consist of three modules, i.e., retinal vessel, (a) segmentation, (b) classi¯cation and (d) width estimation. The accurate segmentation and classi¯cation of retinal vessels directly a®ects the retinal width estimation which is later used for AVR calculation. A vast number of computerized retinal analysis studies have focused on vessel segmentation. [23][24][25] There are a few researches that have focused on detection of vessel bifurcations and crossover points. 26,27 As far as retinal vessel classi¯cation is concerned, there are existing methods that recognize vessels as veins and arteries either automatically or semi-automatically. 28,29 The most prominent visual di®erence between retinal veins and arteries is their color. Arteries are light in color due to the abundance of oxygenated hemoglobin and this fact has led to the use of intensity-based features for vessel recognition. The pioneer study was proposed by Grisan and Ruggeri 88 for arteriovenous classi¯cation in which retinal image was divided into four quadrants based on optic disk center and vessel segments found in each quadrant are classi¯ed using color features. This quadrant division-based approach is also adopted in later studies. 30 In another method proposed by the same group, 31  of vessels in each zone using vessel pro¯le features. A similar approach is proposed by Mirsharif et al. 32 with a little variation by dividing the image in four quadrants with further partitions in upper and lower regions.
Some of the methods presented previously also employed inherited vessel-structure sequence information along with color features for retinal vessel classi¯cation. A method proposed by Niemeijer et al. 33 for classi¯cation of retinal vessels incorporated color features and prior structural knowledge of vessels. Another important inherited characteristic of artery-vein is that the same types of vessel never cross each other. This retinal vessel property has also been employed to classify vessels. 34 Furthermore, in the literature, some methods classify complete vessel network while others consider only small vessel segments within speci¯c circular zone for classi¯cation. 35,36 However, it is not necessary to classify complete vessel network for calculation of AVR. 3 Graph-based methods have been investigated in Ref. 37. In these methods, graphs are generated using vessel center-lines with vessel junction points and the resultant graphs are classied into arteries and veins. Most of these methods classi¯ed the complete vessel network. 38 Same group Dashtbozorg et al. 39 ; Mendonça et al. 40 also proposed methods for AVR calculation. Among the recent methods, Xu et al. 41 proposed¯rst-and second-order textural features for di®erentiation between arteries and veins in retina and Yan et al.
(2017) used context-dependent features for retinal vessel classi¯cation. Quite recently, Relan et al. (2017) presented approach for arteriovenous classication that includes the use of a pre-processing module called multiscale self-quotient image method for illumination and lightning correction in retinal images. Currently, the deep learning network has also been widely and successfully applied in the retinal image processing and segmentation. [42][43][44] Although, the advancement in technology has paved the path for robust and reliable development of computer algorithms for HR detection through assessment of retinal vessels, however, it is observed that the methods previously proposed are tested on healthy retinal images, that do not contain pathological structures. The disease progression makes the retinal vessels prone to many di®erent kinds of pathologies, e.g., vessel tortuosity, hard and soft exudates, branch retinal artery and vein occlusion, sheathing of vessels, focal arteriolar narrowing and optic disk swelling, which deteriorate the width and intensity of vessels. Moreover, HR progression has di®erent e®ect on vein and artery; comparatively arteries are observed to be more a®ected in presence of HR. Figure 2 shows visualization of such cases in enlarged slices of six images, taken from retinal fundus database acquired from Armed Forces Institute of Ophthalmology, Pakistan. Development of new \ghost" vessels and vessel fading is observed due to occlusion in Fig. 2(a). As shown in Fig. 2(b), retinal arteries are hardly visible (e.g., the ones indicated by circle arrow) due to occlusion and sheathing of vessels with appearance of cotton wool spots in fundus area. Optic disk swelling can be noted from Figs. 2(b) to 2(d). Branch retinal vein occlusion is shown in Fig. 2(c) which makes the vessel appearance deteriorated. It is observed that these pathologies pose a serious di±culty in retinal vessel classi¯cation phase, since vessel intensity is the major character that is used to classify vessels. The performance of retinal vessel classi¯cation methods on pathologically diseased images needs to be evaluated so that a robust solution can be devised which is invariant to presence of pathological changes. This paper attempts to provide a system for reliable HR diagnosis using AVR parameter that is robust to presence of pathological structures in fundus images. Furthermore, the features extracted for retinal vessel classi¯cation may contain redundant information. For this purpose, we exploited two feature ranking strategies for feature selection. Feature selection is a technique to obtain dimensionally reduced feature set by retaining only those features which are truly relevant for predicting the outcome. There are a number of ways for selection of most signi¯cant of most features from a large feature set. Most widely used among these ways are; (a) Wrapper methods: Feature selection based on association between predictors (features) and responses (target labels) before applying machine learning algorithm and (b) Filter methods: Feature selection after applying machine learning techniques. In the¯rst type, signi¯cant features are¯ltered out from the original dataset by evaluating the relevance of individual attributes (features) with the target classes. The criterion according to which the feature-target relationship is measured depends upon the speci¯c feature¯ltering algorithm. Whereas in second type of feature selection techniques, attribute selection is conducted on the basis of performance of feature in predicting the target class after it has been fed to classi¯er. Using this technique for feature selection, a feature may show optimal performance for a certain classi¯er but fails to perform optimally for other classi¯ers. E®ect of¯lter-based feature selection methods for anomaly detection is examined in depth in many medical applications [45][46][47] and promising results are reported. The impact of feature ranking methods in relation with decision mapping of machine learning algorithms for Artery/Vein (A/V) classi¯cation needs to be evaluated.
In addition to the feature selection process, the class prediction performance of retinal vessels also depends signi¯cantly on the particular machine learning algorithm. In methods proposed by, Relan et al. 48 53 for retinal vessel classi¯cation, but this ensemble system is created by employing one type of base classi¯er. In bootstrap method, di®erent predictive models are generated using di®erent subsets of data and then the decisions of all those models is averaged out. Fusion of di®erent classi¯ers decisions is known to have enhanced performance as compared to single classi¯er and has been used in many machine learning applications. [54][55][56][57] This motivated us to examine the performance of di®erent classi¯ers combination for retinal vessel classi¯cation.
With respect to the issues highlighted above, this paper aims to develop an automatic framework for detection of HR with an improved retinal vessel recognition module which is based on the use of di®erent feature ranking strategies and classi¯cation accuracy of various prediction models (k-Nearest Neighbor, Support Vector Machine and Naïve Bayes) to select optimal feature subset followed by vessel labeling through the proposed hybrid classi¯cation approach. Moreover, the proposed system detects HR robustly not only in healthy images, but also in images with multiple pathological changes. This research allows to investigate the impact of proposed feature selection process and decision-fusion of multiple classi¯ers on labeling of retinal vessels. The e®ect of proposed method on retinal vessel di®erentiation is evaluated using three performance metrics, i.e., Classi¯cation Accuracy, Sensitivity and Speci¯city and the method is tested on three databases, Local Database, INSPIRE-AVR database 33 and VICAVR database. 31 The performance of AVR calculation module is assessed by calculating the mean error between the estimations provided by ophthalmologist and the ones shown by our method. The promising results presented by proposed system shows its capability in lowering the prevalence of HR and can be proved a valuable tool for retinal screening.
Main contributions of this work are: (a) The robustness of proposed retinal vessel clas-si¯cation method and subsequent HR diagnosis is examined in images with pathological structures. Currently, there are seldom papers that report hybrid classi¯cation approaches on retinal fundus photography with HR. The proposed system detects HR robustly not only in healthy images but also in images with multiple pathological changes. (b) A novel feature selection strategy that includes lter-based methods with the use of three classi¯ers for selection of optimal feature subset is employed. The feature ranking is carried out using two feature ranking algorithms, Pearson Correlation Coe±cient 58 and Relief-F method, 59 to rank the features (extracted for A/V di®erentiation) and then, employing classi¯cation accuracy of three supervised classi¯ers as a stopping criteria (threshold) to select the optimal feature subset from ranked feature list. (c) The proposed \labels-combination" framework has been investigated for recognition of retinal vessels. Majority voting technique is used to combine the decision labels obtained from three classi¯ers, i.e., k-Nearest Neighbor (k-NN), Support Vector Machine (SVM) and Naïve Bayes, for vessel labeling. This paper contains¯ve sections; introduction and review of previous work is already explained in this section, Sec. 2 explains the methodology adopted for retinal image preprocessing, vascular network extraction, Optic Disk localization and boundary segmentation, determination of region of analysis, feature extraction for vessel recognition and¯nally blood vessel width calculation for AVR computation. Section 3 focusses on the details of feature selection process and retinal vessel classi¯cation followed by experimental results in Sec. 4. Section 5 summarizes the contributions and limitations of this research.

Methodology
The°ow chart for the proposed methodology is shown in Fig. 3. The retinal image is¯rst acquired via fundus camera and then preprocessed. After that, the retinal vascular network is detected using Gabor¯lter bank and a binary vessel map is generated. Details of preprocessing and vessel segmentation is given in Secs. 2.1 and 2.2, respectively. Next, the position of optic disk is determined using Laplacian of Gaussian¯lter with highest vessel density feature. Based on the optic disk boundary, a circular region of interest is de¯ned around optic disk and the vessels within this region are obtained, as described in Secs. 2.3 and 2.4 Vessel junctions i.e., bifurcations and cross-overs, present in the extracted vessel segments are detected and then, di®erentiated using local variance based method in order to remove cross-overs. In the next step, a set of 81 features is extracted from retinal vessels as explained in Secs. 2.5. The acquired features are then subject to two feature-ranking methods, i.e., Pearson Correlation Coe±cient and Relief-F method. Di®erent combinations of ranked features are then fed to three supervised classi¯ers (k-NN, SVM and Naïve Bayes) and based on the classi¯cation accuracy of each classi¯er; optimal feature subsets are selected and fused together using union operation. Afterwards, these fused feature subsets are given as an input to decision-fusion framework and nal labels of retinal vessel segments are obtained. Classi¯ed vessel segments are then measured using 2-Dimentional (2D) Euclidean distance transform, as explained in Sec. 2.6. After measuring the widths of vessel segments, AVR is calculated. Details of feature ranking algorithms, classi¯ers and feature selection method are given in Secs. 3.1 and 3.2, respectively. Experimental results and performance comparison are presented in Sec. 4 followed by discussion in Sec. 5. The proposed methodology involves technically diverse techniques for each step from image preprocessing to calculation of AVR and some steps involve tuning of relevant parameters which a®ects the¯nal performance of the system. In addition to that, all three image datasets used in this research have di®erent image speci¯cations (size and quality); therefore, in some steps, optimal parameter values may vary. The tuned parameter values are mentioned explicitly where they are di®erent for the three datasets.

Preprocessing
As a preprocessing step, dark background is segmented from digital fundus image in order to reduce the computational complexity. The background is estimated using local mean and variance-based method 60 and binary segmentation mask is formed by thresholding operation, which is dependent on mean of green component of image. The generated background mask is shown in Fig. 4(b) with original image in Fig 4(a), taken from local and INSPIRE-AVR dataset (in¯rst and second row, respectively). Local and INSPIRE-AVR datasets are tuned at a threshold value of 10 whereas for VICAVR dataset, this threshold is set at 30 after background estimation. Regarding threshold selection, we adopt trying and testing techniques, in order to¯nd the binary images with whole retinal information.

Vessel extraction
2D Gabor¯lter bank is employed here for extraction of vessels. 61 The purpose of using Gabor Wavelet bank is its localization characteristic, due to which the response on small as well large width vessels are captured with greater accuracy. Gabor Wavelet is applied on green channel of image due to the e®ective discrimination between retinal vessels and fundus area present in this color component. After enhancement of retinal vessel tree, it is thresholded. The Gabor Wavelet is computed for angle spanning from 0 up to 179 at steps of 10 and then the maximum response (MR) is taken. A scale value of 7, 9 and 11 is found to be optimal for local, INSPIRE-AVR and VICAVR dataset, respectively. By varying the angles and scales, Gabor¯lter bank is formed which enhances the objects in target image according to the set parameters. Figures 4(c) and 4(d) show the enhanced vascular patterns in retinal images using Gabor Wavelet and the binarzied vessel trees, respectively.

Identi¯cation of the position of Optic Disk (OD)
OD is a bright circular region in retina from which all the blood vessels emerge. Laplacian of Gaussian (LoG)¯lter and the highest vessel density property of OD is used in this research to detect the location of OD. 62,63 LoG¯lter is applied on red channel of RGB image to enhance the location of OD. This template is particularly used because of circular structure of OD and red channel is selected because of clear and discriminating visualization of OD in this channel. After the candidate circular regions have been enhanced using the LoG¯lter, they are binarized. The threshold value used for binarization is given in Eq. (1). 61 This threshold selects pixels having top 60% response from the LoG¯ltered image and mLoG indicates the maximum value in Gaussian Kernel Processed Image. 62 Preliminary experiments guided the selection of this threshold since it is optimal for all datasets. Red plane of original retinal image, LoG¯lter, enhanced OD region and binarized OD is shown in Figs. 5(a)-5(d), respectively. Some images in the local dataset contain pathologies like hard exudates and cotton wool spots that have similarity in structural and color properties with OD, so the LoG¯ltered and subsequent thresholded image may contain more than one OD region. To overcome this issue, vessel density property is incorporated to separate out the OD region from the other segmented portions. After localization of OD position, as illustrated in Fig. 6, its center is determined and boundary is estimated using intensity gradient based technique which we recently proposed in Ref. 63.

Determination of \Analysis Zone" and extraction of vessel segments from vascular tree
Once the position and boundary of OD is determined, a Region of Analysis (RoI) is identi¯ed for extraction of candidate retinal blood vessels which are to be categorized into artery or vein class. As suggested by Parr and Spears, 64 Knudtson et al.
(1994) a circular zone that is at a speci¯c distance from OD, is marked and the vessels within this zone are considered for classi¯cation and AVR computation purpose. Although, some of the researchers have classi¯ed the complete retinal vessel network 37,39,52 but since our goal here is to calculate AVR which can be e±ciently calculated by assessing the blood vessels in a speci¯c circular zone around OD, therefore, only the vessel portions within a circular zone are selected. A¯xed circular RoI around OD is identi¯ed by placing two concentric circles; one at 1=4 Disk Diameter (DD) and another at 1 DD, from OD boundary. Another reason for selection of this zone is to ignore the vessel portions near OD because glial tissue or perivascular sheathing may in°uence the vessel segments in OD proximity. 11 Figure 7(a) shows the OD boundary and RoI between the two concentric circles and Fig. 7(b) shows the vessels extracted from measurement zone. After the vessels within RoI are extracted, the next phase is to split those connected vessels into isolated vessel segments by determining the vessel junction points (bifurcations and cross-overs). These landmarks make the vessel classi¯cation and measurement task ambiguous. The slices in Fig. 9 illustrates this phenomenon where by examining it can be noticed that the arteriovenous crossing in vessel center-lines appears as one vessel segment, shown in Fig. 9(c). In order to rectify the false landmark, it is important to di®erentiate between bifurcations and cross-overs. Moreover, even for AVR calculation, the arteries and veins needed to be properly distinguished, therefore the vessels with crossing points must be isolated into individual vessel segments. In this paper, we adopt a local variance-based method for di®erentiation between two types of junction points. For determination of these junction points, following steps are implemented.
. First, the binary vessel map is skeletonized and then potential junction points are extracted. Skeletonization is an operation that removes the pixels from edges of objects without destroying the connectivity in an eight-connected scheme and as a result, one-pixel wide center-line vessel structure is extracted. 23 For skeletonization, a level-set algorithm proposed in Rumpf and Telea, 66 is used. The reason for choosing this method is that it gives more smoother and centered structures than other thinning methods. Moreover, center-line vessels avoid pruning branches via this algorithm. Figure 8(a) show the center-line vessels and (b) center-line vessel structure embedded on RGB retinal image. . Then, this skeleton-vessel image is convolved with a kernel of 3 Â 3 shown in Fig. 10(a) and for each pixel, the number of neighboring pixels are counted. The location of pixels which have three or more than three neighbors is taken. These locations indicate vessel junction points, i.e., bifurcations, arteriovenous crossings or crossing between vessel and capillary. Figure 10(b) shows the pixel localized that have three or more than three neighbors whereas (c) shows a single arteriovenous crossing which appears as two bifurcation points. . Now, to di®erentiate between a junction that is bifurcation or arteriovenous crossing, the local variance-based method is used. A circular window of radius 11 is employed here that is made centered on the detected junction points (as shown in Fig. 10(d), where the junction points are shown in red with a circular window in green. The variance of pixels inside the window in green component of RGB image is captured. Since the vessel crossings do not contain pixels from just one type of vessel, i.e., it either contains pixels from (artery and vein) or (artery and capillary) or (vein and capillary), the captured variance will show a spike in variance if it is a cross-over and will have more variance than bifurcation points. This variancebased property is used here to characterize the vessel junctions as cross-overs or bifurcations. . Once the bifurcations and crossing-overs have been di®erentiated, the cross-over points are eroded in original extracted vessel map. As a result, we will have an image that does not have vessel cross-overs.
It should be noted that for detection of cross-over points, di®erent structures with varying radii were tested and the preliminary trials favored the choice of circular window with radius 11. After the cross-overs are identi¯ed and removed, the binary image now contains veins, arteries and small thin capillaries. However, due to unavailability of ground truth, the thin capillaries are not considered in next phase, i.e., feature extraction for vessel classi¯cation.

Feature extraction for vessel classi¯cation
Once the vessel tree is split into vessel subsegments, features are extracted from each candidate vessel segment. Each detected vessel is regarded as a sample for classi¯cation and represented by a feature vector containing several features. In previous work, we proposed method for vessel classi¯cation. 67 However, the research was tested on a small image dataset that does not contain any pathology. In another approach, 68 retinal vessels were classi¯ed using a small number of vessel segments from each dataset (major A/V pairs).
In this paper, 81 features are proposed for representation of blood vessels in retina, i.e., a single vessel sample is represented by 81 features. Although, the use of large number of visual representations for a pattern recognition problem increases the probability of accurate object classi¯cation, but it also increases the computations involved in extracting and categorizing those features. However, our proposed method includes the feature selection process, so any irrelevant features extracted will be removed before¯nal vessel labeling. Let  distribution of gradient magnitude representing the changes in vessel intensity with respect to fundus area pixels. (III) Features based on¯lter responses, where the¯lters borrowed from Leung and Malik, 69 Schmid, 70 Geusebroek et al. 71 These features are extracted from either vessel centerlines or complete vessel segments. Features extracted from vessel center-lines are e®ective due to the presence of light re°ex in center of arteries and this light re°ex in arteries makes them distinguishable from veins since veins are darker in intensity. Another reason for widely use of features from center-lines is the less number of pixels required in feature set which leads to less computations in form of pixel-processing as compared to features from complete vessel segments. RGB, CIE L*a*b, CMYK and YCbCr color spaces are exploited for extraction of features. All the features are concatenated into a single feature set, consisting of 81 features. It has been observed in literature that features obtained using di®erent methods outperform single type of features because visual representations acquired using multiple techniques have the ability to capture various aspects of same object in image. 72,73 Details of proposed features are elaborated below and Table 1 tabulates the features which are used in this paper for retinal vessel recognition.

Histogram-based¯rst-order statistical features
First-order statistical features are extracted using histogram of vessel center-lines. The vessel centerline pixel intensities are recorded in di®erent color spaces and saved into a vector. Then the distribution of vessel center-line pixel intensities is analyzed by quantizing the total intensity range into 256 bins. The motivation behind extracting features from histogram-based statistical values is that they o®er better results as compared to raw pixel values. 74 21 features are extracted using statistical properties of intensity distribution as described in Table 1.

Vessel Intensity Transition Features (VITF)
VITF represents strength of change in intensity as the circular pro¯le crosses the vessel segments, illustrated in Fig. 11 and this strength is expressed here by means of gradient magnitude. Gradient magnitude accurately depicts the power of peaks and valleys of intensity in an image. The cross-sectional vessel intensity transitions are investigated in depth here. As mentioned before that arteries are  brighter in intensity as compared to veins, so the intensity transitions captured for both classes (artery and vein) show signi¯cant di®erence. It should be noted that the curved pro¯le is made to obtain features from all those vessel segments which are considered in RoI for vessel classi¯cation. For extraction of the transition features, a portion of circle cutting the vessel segments is taken and gradient magnitude of intensities along with that curved portion is calculated as shown in Fig. 11. The strength of gradient magnitude for vein class is larger due to abrupt changes in intensity of vein, whereas for artery class, they are lower because arteries are brighter as compared to veins so intensity transitions are not sharp as compared to fundus area pixels. Therefore, the gradient magnitude will be high for vein class as compared to artery class. This is characterized by considering the minimum and maximum value of gradient magnitude. Also, the spatial distribution of gradient magnitude is obtained and quantized into 15 bins. It is noticed that for vein class, the majority of values cluster at starting and ending bins in spatial distribution while for artery class, magnitude gradient values show membership to the bins which are in middle. Moreover, the gradient magnitude values for the artery class are evenly distributed among all bins as compared to vein class, so this behavior is captured by taking kurtosis and variance of gradient magnitude histogram. We further explain this property as follows: As the vein class shows wider blood vessels than artery class, the gradient magnitude is higher along its edges, but lower within its internal pixels. While for artery class, as the width of blood vessels is very narrow, the variation in gradient magnitude is less, so its spatial distribution Leung-Malik¯lter bank contains; 48¯lters including¯rst and second derivative of Gaussian lters at various orientations and scales, Laplacian of Gaussian¯lters and simple Gaussian¯lters. However, we have borrowed only one Gaussian¯lter which is at scale ¼ 2 p 2. The selection of this lter is made through the preexperiments in which only one¯lter was seemed to enhance the retinal vessels.
Schmid¯lter bank contains 13 rotationally symmetric¯lters of the form given in Eq. (2).

Width estimation of vessels
The width of classi¯ed vessel segments is calculated here using 2D Euclidean distance transform. 75 When the distance transform of a complement of binary image is taken, the resultant image looks like a gray-level image, but in actual distance-transformed image represents distance of the respective pixel to the nearest nonzero pixel. For calculation of width,¯rst the complement of segmented binary vessel image is taken (say I 1 ) shown in Fig. 12(b). 2D Euclidian distance transform is applied on I 1 in Fig. 12(b), giving I D as a resultant image shown in Fig. 12(c) with its enlarged version. Then the center-line vessel map of original binary vessel network I B is obtained, as shown in Fig. 12(d) and multiplied with I D to acquire distance map value for center-line pixels. This distance map image (shown in Fig. 12(e)) is¯nally multiplied by two to get vessel width.  Fig. 12(e). Therefore, mean of width of a vessel segment is taken and collected in separate vector; \Arteriole" and \Venule", respectively, depending upon the class of label of vessel generated previously. These two vectors show the mean width of respective vessels. Equations (3) and (4) show the formula for calculating CRAE and CRVE, respectively.

Calculation of AVR
where W b and W a , is the median and the value occurring immediately before the median in vector \Arteriole", respectively.
Likewise for CRVE, W b and W a is the median and the value occurring immediately before the median in vector \Venule", respectively. AVR is calculated as given in Eq. (5).

Feature Selection and Classi¯cation of Vessels
In this section, the method proposed for feature selection and vessel classi¯cation is explained. To select the signi¯cant features, the features are¯rst ranked using two feature ranking strategies and then the classi¯cation accuracy of three classi¯ers is used as a threshold to select an optimal feature subset from ranked feature list. The feature subsets selected depending on accuracy of each classi¯er are then fused to make a single feature subset and will be used by hybrid labeling method for retinal vessel classi¯cation. This process is elaborated in detail in sections to follow. We will¯rst discuss the feature selection process here followed by vessel classi¯cation scheme.

Ranking of features and selection of optimal feature subset
The motivation for including a feature selection module is that the extracted features may contain some redundant data that leads to over¯tting of prediction model and consequently reduction in prediction accuracy. The selection of features ensures the inclusion of only those features that are actually useful for classi¯cation and subsequently decreases the computational complexity. 76 In this paper, we use two feature-ranking techniques to rank the features but a novel approach is followed for selecting features from ranked feature list. The system works by¯rst ranking the features according to two feature ranking methods, i.e., Pearson Correlation Coe±cient 58 and Relief-F method 59 and then selection of optimal features. Generally, after the features have been ranked and arranged according to their ranks, a speci¯c threshold is used to select a certain number of top-ranked features. This threshold is usually user-de¯ned, however, as pointed out in Refs. 77 and 78, the correct way to ensure the selection of optimal combination of topranked features is by evaluating the classi¯cation performance of di®erent combinations of top-ranked features. Therefore, the selection of signi¯cant features from a ranked feature list cannot be carried out using a¯xed threshold because we do not have a prior knowledge regarding the performance of different number of ranked features. In this paper, we use the maximum classi¯cation accuracy of classiers as the threshold to select the features. A particular number of top-ranked features that yield maximum accuracy on classi¯er is selected. In this paper, we employed three classi¯ers for selection of optimal number of top-ranked features. The optimal feature subsets selected using three classi¯ers are combined and used by proposed hybrid classication technique for vessel classi¯cation. Class label y i and feature value f j of every sample x i is given as an input to feature ranking strategy. Both these techniques evaluate correlation of each feature with the class label using some criteria 79,80 and a rank is generated for each feature. The features are then arranged in descending order of their ranks, i.e., F ¼ ff r 1 ; f r 2 ; f r 3 ; . . . ; f r N g, where f r 1 and f r N denotes the features with highest and lowest rank, respectively. For selection of feature subset, the ranked features F are given as an input by constructing \n" feature subsets, in which¯rst feature subset is initialized by incorporating only the highest-ranked feature, the second subset is constructed by adding second topranked feature in the¯rst subset and this process is repeated until the last feature subset contains all ranked features. By applying di®erent combinations of highly ranked features to classi¯ers, different predictive models are generated which have di®erent accuracies. The optimal predictive model is the one with maximum classi¯cation accuracy and the feature subset corresponding to this predictive model is selected. This feature selection process is shown in Fig. 13. As illustrated in Fig. 13, di®erent combinations of ranked features are applied to classi¯er, and the feature subset, f T S , corresponding to maximum classi¯cation accuracy, T, is selected. Now, since we have employed three supervised classi¯ers, so three optimal feature subsets are obtained. The number of features in the optimal subsets is not speci¯c. This hybrid approach allows us to select di®erent feature combinations from ranked feature list. The ranked optimal feature subsets obtained using Pearson Correlation Coe±cient method on k-NN, SVM and Naïve Bayes classi¯er are denoted by f p 1 , f p 2 and f p 3 , respectively, and those obtained using Relief-F method on k-NN, SVM and Naïve Bayes classi¯er are denoted by f p 1 , f p 2 and f p 3 , respectively. Finally, the union of those optimal feature subsets is taken as given in Eqs. (6) and (7), and the resulting feature subsets, F P and F R are used by proposed hybrid classi¯cation scheme for retinal vessel labelling. The feature ranking approaches used are ð6Þ

Pearson Correlation Coe±cient method
The Pearson Correlation Coe±cient (PCC) method ranks features by calculating linear correlation between individual features and class labels. 58 In this paper, we use PCC method to obtain rank of features. This PCC method¯nds correlation p i for relevance assessment of the feature f j with the corresponding class label y i and as an output, a correlation score for each individual feature is generated. PCC of a vessel sample x i (where x i 2 X) and class label y i (where y i 2 Y ) is calculated as given in Eq. (8), where cov is covariance and is variance.

Relief-F algorithm
The second feature ranking algorithm that is used here is Relief-F algorithm. 59 In Relief-F algorithm, each feature gets a weight depending upon its strength for distinguishing between those opposite class samples that are near to each other and di±cult to di®erentiate. The feature rank is calculated by taking a data point at random and considering the k-nearest neighbors of that data point. 59 The k-nearest neighbors are taken from both the classes and by considering their contribution, the strength of feature is analyzed. In order to¯nd the optimal value of k for this feature ranking technique, we analyzed the weights of features by varying the value of k. Here, maximum value of K is taken as 75% of total instances because according to theory of Relief-F concept, 59 if the value of K is taken too small, then estimates would be di±cult to generalize on highly varied data whereas if the value of K is equal to number of instances, then signi¯cance of relevant features will be deteriorated.

Details of classi¯ers used for feature selection after ranking of features
After the features are ranked using the above mentioned strategies, signi¯cant features are selected by application of ranked features on three classi¯ers (k-NN, SVM and Naïve Bayes). The same three classi¯ers are used in decision fusion framework for recognition of retinal vessels. The purpose to use the same classi¯ers for vessel classi¯cation, is to study the e®ect of single classi¯ers performance with the ones obtained when they are combined. The classi¯ers used are detailed in what follows. Fig. 13. Complete framework for optimal ranked features selection, where f N S represenets the total number of feature subsets acquired from ranked feature list, Acc N S denotes the classi¯cation accuracy corresponding to feature subset f N S , T represents the maximum accuracy obtained using a feature subset f T S .

k-NN classi¯er
k-NN is one of the simplest classi¯ers used for supervised classi¯cation. 81 It searches for closest k samples from complete dataset by calculating distance between training and test instances. For example, in our case, when an unknown vessel sample, say x i comes, the labels of k-nearest neighors of x i are analyzed and then x i is assigned a class (either \artery" or \vein") depending upon the label of majority neighbors. The distance between the test sample and all nearest neighbors is calculated. \Euclidean distance" is chosen to calculate the distance between sample and neighbors. Equation (9) shows the Euclidean distance calculated between the vessel sample and its nearest neighbors, where x i is the test sample and x mb represent the nearest neighboring samples with subscript b showing the total number of nearest neighbors. In order to obtain the optimal value of k for our vessel classi¯cation task, di®erent k values such as 1, 3, 5, 7 and 9 are tested.

SVM classi¯er
SVM is a supervised machine learning method that separates di®erent classes in testing data by an optimal hyperplane 82 and the advantage of using SVM in classi¯cation lies in its ability to identify a nonlinear separation between data-points of di®erent classes. This is carried out by using di®erent \separation" functions called kernels. The input sample vector x i represented by N feature values is mapped to a new feature space ' with higher demensions and an optimal hyperplane is constructed using the kernel Kl(x i ; x m ), shown in Eq. (10), where x i and x m are two feature input vectors. In our case, the dataset is tested using SVM with di®erent kernel functions, i.e., Polynomial (Kl po ) and Radial Basis Function (RBF) (Kl Ga ), and the function that provides optimal results is selected. For polynomial kernel, the degree is varied from 1 to 3 and for RBF kernel, the scaling factor is tested using values from 1 to 9. The representations for both these kernel functions are given in Eqs. (11) and (12). 83 Klðx i ; x m Þ ¼ h'ðx i Þ:'ðx m Þi; ð10Þ where is degree of polynomial (11) where G is Gaussian sigma.

Na€ {ve Bayes classi¯er
Naive Bayes classi¯er is a widely used probabilistic classi¯er that classi¯es the data based on Bayes' Theorem. 84 The input data matrix X and vector of labels Y are fed to classi¯er, and according to Bayes theorem, the classi¯cation aim is to achieve maximum probability P ðY jXÞ, as shown in Eq. (13). The strength of Naïve Bayes is its simplicity and e±ciency with which it classi¯es the data. Naïve Bayes classi¯er is implemented using di®erent distribution functions such as kernel and normal. The classi¯er is tested with both distribution functions and model with highest validation accuracy is selected.

Proposed hybrid classi¯cation scheme
The proposed hybrid classi¯cation technique is a fusion of decisions generated by k-NN, SVM and Naïve Bayes classi¯ers for vessel classi¯cation. The proposed scheme works in a way such that the labels given by each of three classi¯ers are acquired and a¯nal label is assigned to the vessel sample by a classi¯er fusion technique known as majority voting. 85 The main motivation for combining the decisions of the supervised machine learning methods is the strategy used for decisions combination, which re°ects the local competency of individual learning methods. 86 Moreover, the samples mis-classi¯ed by individual classi¯ers may not necessarily overlap. 87 Majority voting is one the popular classi¯er fusion techniques in which the single labels produced by individual classi¯ers are counted and the sample is given the label with majority votes. 87 It is an e±cient classi¯er fusion scheme since it does not require any other information except for single class labels generated by individual classi¯ers. The optimal feature set selected by the feature selection process is used by proposed hybrid classi¯cation method for vessel di®erentiation.

Experimental Results
Through experimental results, we aim to investigate if the proposed feature selection and classi¯er fusion technique improves the retinal vessel classi¯cation task and subsequent AVR calculation. We¯rst give a description of datasets used in this research. Then, we elaborate the procedure for choosing the optimal parameters of classi¯ers. Afterwards, we illustrate the feature ranks obtained from two di®erent strategies and features selected after application of ranked features on classi¯ers. Then, we show the results of applying selected features on proposed decision combination framework followed by AVR calculation results. Computer program in this work is implemented using computer with 1.80 GHz processor and 4.0 GB RAM. Commercial software MATLAB is used for implementation purpose.

Speci¯cations of datasets
The methodology is evaluated on three databases: a database collected from Armed Forces Institute of Ophthalmology (AFIO), Pakistan, and two public labeled databases, i.e., INSPIRE-AVR 33 and VICAVR database. 31 In this research, only those vessel segments are used for retinal classi¯cation and quanti¯cation purpose whose labels are provided in ground truth. The local database contains 44 retinal images in JPEG format with dimensions 1504 Â 1000, including 11 images containing pathological structures like hard exudates, cotton wool spots, hemorrhages, arteriosclerosis, vessel tortuosity, focal arteriolar narrowing and OD blurring. True vessel labels and AVRs are acquired by an expert ophthalmologist that will be are considered as a ground truth. INSPIRE-AVR is a publically available database containing high-resolution 40 OD centered healthy retinal images, acquired at the University of Iowa Hospitals and Clinics. These images are of size 2392 Â 2048 and available in JPEG format. AVR values estimated by two observers are provided with INSPIRE-AVR database, to be used for comparison and the vessel labels are acquired from our ophthalmologist. Third database used is VICAVR that contains OD-centered 58 images of size 768 Â 576. The artery-vein labels and vessel caliber for VICAVR database, obtained from three human experts are available with the dataset. Table 2 describes the complete speci¯cations of datasets used in this study.
The images in local dataset are marked by ophthalmologist on the basis of visual appearance; therefore, underlying causes of di®erent abnormal structures are not exploited here. Additionally, detection and diagnosis of the other retinal pathologies occurring independently or associated with HR are beyond the scope of this research. In this paper, we have evaluated the results only for vessel clas-si¯cation and AVR computation. The unclassi¯ed vessels are not included in evaluation.

Parameter tuning of classi¯ers
In our research, classi¯cation accuracy of three classi¯ers (k-NN, SVM and Naïve Bayes) is used as a threshold to select the optimal top-ranked features. Before giving ranked features as an input to classi¯er, for feature selection, the parameters of classi¯er are tuned. This is done in \parameter tuning phase", where the dataset is divided into two parts, training set (70% of data) and validation set (30% of data). The classi¯er is tested with di®erent parameters using training data and then accuracy is evaluated on validation set. Complete ranked feature set of 81 features is given as input to classi¯er for tuning of parameters. The parameters showing maximum accuracy on validation set are selected. All three supervised classi¯ers are trained once using training data and then tested on validation set to acquire optimal parameters. The values of optimal parameters of classi¯ers are mentioned in Table 3.
Once the optimal parameters are acquired, three classi¯er models (k-NN, SVM and Naïve Bayes) are re¯t again to entire dataset using 10-fold cross validation and classi¯cation accuracy of these three classi¯ers is used to select optimal number of ranked features from ranked feature list. In 10-fold crossvalidation, data is divided into 10 subsets, out of which nine are retained for training and one is used for testing. The samples which are included in each fold are randomly selected. Each fold is iteratively tested and the rest of folds are kept for training. The 10-fold cross-validation is conducted for 10 times, and the samples which are included in each 10-fold cross-validation are randomly selected di®erently. Di®erent combinations of ranked feature subsets are given as an input to classi¯er and the subset leading to maximum classi¯cation accuracy is selected. The performance metrics calculated for evaluation of ranked feature subsets on classi¯ers are, accuracy, sensitivity and speci¯city. However, accuracy metric is used as a stopping criteria to select the number of top-ranked features from ranked feature list or in other words, as a threshold to select the optimal feature subset. Sensitivity the is true positive rate (positives) and speci¯city is true negative rate (negatives). The feature selection procedure is illustrated in Fig. 13. The evaluation parameters are calculated using Eqs. (14)-(16), respectively.

Performance of feature raking methods and Selection of optimal features
In order to rank the features using Relief-F method, the value of K, i.e., number of nearest neighbors is determined. We analyzed the weights of features with varying the number of nearest neighbors, i.e., K ¼ 1 to 250, 1 to 287 and 1 to 333, for local, IN-SPIRE-AVR and VICAVR datasets, respectively. The optimal value of K for which the weights of features become stable is 196, 132 and 245 for local, INSPIRE-AVR, and VICAVR dataset, respectively. Figure 14 shows the sample plots of¯rst 24 features from local database. The ranking of features depends on the weights, and Fig. 14 shows the weights of features are varying with increasing the number of K-neighbors. It can be observed in Fig. 14(a) that the feature 1 has a signi¯cant weights di®erence with other 5 features (i.e., from Table 3. Parameters con¯guration for di®erent classi¯ers.

Classi¯ers
Classi¯er parameters selection using features ranked by both methods k-NN Nearest neighbors k ¼ 3 SVM \RBF" kernel with scaling factor 7 Naïve Bayes \kernel" distribution function  Fig. 14(b), it is observed that the weights of feature 7 are increasing with an increase in number of neighbors. It can also be observed that as K approaches 196, the feature weights become stable. This situation motivates us to select K ¼ 196 for local database, since adding more neighbors is not contributing towards the better modeling of data. For selection of top-ranked features, di®erent subsets of features acquired from ranked feature lists are applied on k-NN, SVM and Naïve Bayes classi¯er using 10-fold cross-validation. This lead to generation of 81 predictive models with di®erent accuracy, sensitivity and speci¯city metrics, as illustrated in Fig. 15 with upper and lower curves showing performance metrics for local and IN-SPIRE-AVR dataset, respectively. The feature subset that maximizes the classi¯cation accuracy on each classi¯er is selected. For a better visualization and comparison purpose, we concatenated the performance curves of both datasets on same x-axis in Fig. 15. From these illustrations, the relation of classi¯er with certain combinations of ranked features can be observed. Each classi¯er's response for each feature subset is di®erent, which indicates the importance of features combination on the class label outcomes. Use of di®erent classi¯ers for selection of optimal number of features, resulted in selection of feature subsets containing di®erent number of features. For example, as shown in Fig. 16(a), the feature subset that led to maximum classi¯cation accuracy on k-NN, SVM and Naïve Bayes classi¯er for local dataset using PCC, consists of di®erent number of features, i.e., 45, 55 and 51, respectively. These feature subsets will be combined using union operation to obtain a¯nal feature subset.
In terms of number of features, no speci¯c pattern is seen among the number of features in optimal subsets in Fig. 16. However, in majority cases, SVM requires the largest number of features to reach the maximum classi¯cation accuracy. In all cases, the value of \threshold" (maximum classi¯cation accuracy), is highest for INSPIRE-AVR database. An obvious explanation for this observation is the greater quality of fundus images in INSPIRE-AVR dataset. From Fig. 15, it is also concluded that overall no signi¯cant di®erence is seen between the performance of classi¯ers on features ranked either using PCC or Relief-F method. We also tested if the use of feature ranking is bene¯cial by analyzing the e®ect of feature subsets obtained from; (a) Ranked features list using Relief-F method, (b) Raw feature list without using ranking algorithm, on k-NN classi¯er for VICAVR database. From Fig. 17, it is found that feature ranking strategies have actually contributed in increasing the classi¯cation accuracy. Note that the average accuracy and peak accuracy attained from ranked list is much higher as compared to accuracy illustrated using unordered feature list.

Optimal feature subset selection
Since we use classi¯cation accuracy generated by three classi¯ers as a criteria to select optimal feature subset, so three di®erent feature subsets will be selected for each dataset. As it can be seen in Fig. 16, the number of features showing maximum classi¯cation accuracy on each classi¯er is di®erent, even for the same dataset. So, in order to have a single feature subset that can be used by proposed hybrid classi¯cation approach, we combine the feature subsets acquired using di®erent classi¯ers. The number of features in each subset resulted after talking union are shown in Fig. 18. The exact features in selected subsets are shown in Table 4. Majority of features in feature subset selected using PCC with preevaluations by three classi¯ers are also present in feature subset acquired using Relief-F method. This indicates the similarity in ranking of two di®erent strategies.

4.4.
Retinal vessel classi¯cation using proposed hybrid classi¯cation scheme with optimal feature subset The proposed hybrid classi¯cation scheme combines the labels generated by three classi¯ers, i.e., k-NN, SVM and Naïve Bayes. This decision-combination is chosen for vessel classi¯cation because it represents the joint strength of objective function of multiple classi¯ers. In majority voting, the votes given by each classi¯er for a certain sample are counted and the class with maximum votes is assigned to the sample. For example, if SVM and Naïve Bayes assigns \Artery" to a sample whereas k-NN assigns \Vein", the¯nal label will be given as \Artery", since the \Artery" class has two votes. After assigning the labels using proposed hybrid classi¯cation method, accuracy, sensitivity and speci¯city is calculated by comparing the¯nal labels with ground truth. The classi¯cation performance achieved using proposed decision fusion framework with optimal feature subsets (F P ) and (F R ), acquired using PCC and Relief-F method, is given in Tables 5 and 6, respectively. Overall, hybrid classi¯cation scheme has caused to increase the vessel classi¯cation accuracy, both for feature subsets acquired from PCC and Relief-F ranking list.
We have illustrated the increments in classi¯cation accuracies obtained with proposed classi¯cation technique with those acquired single classi¯ers associated with averaged classi¯cation accuracy on same feature subsets, as shown in Figs. 19 (using PCC) and 20 (using Relief-F). For all datasets, the increase in vessel classi¯cation performance show the improvement induced by the multi-classi¯er decision combination. Confusion matrix attained using the performance measures are shown in Fig. 21. Confusion matrix is a representation of overall classi¯cation performance, and re°ection of the fraction of two classes being correctly classi¯ed or misclassi¯ed. These illustrations validates the ability of proposed system in classifying vessels. Here, we represent the class of artery and vein sample with \1" and \0", respectively. Therefore, the top two entities on the left diagonal of confusion matrix (in green color) are True Negative (TN) and True Positive (TP), respectively. In our case, TP and TN, is the fraction of vessels being correctly classi¯ed as, arteries and veins, respectively, by the proposed method. The other two entities in the adjacent diagonal (in peach color) represent the False Negative (FN) and False Positive (FP), respectively. We represent FP and FN, as the fraction of veins being misclassi¯ed as arteries and fraction of arteries being misclassi¯ed as veins, respectively. The¯rst two entities in third row of confusion matrix represent the Sensitivity and Speci¯city, respectively. In our case, Sensitivity represents the percentage of TP (vessels correctly classi¯ed as arteries) and Speci¯city represents the percentage of TN (vessels correctly classi¯ed as veins). The last entity in the third row on right side represents the overall classi¯cation accuracy. Here, it represents the percentage of all vessels being correctly classi¯ed. The other two entities in confusion matrix on extreme right side of¯rst and second row are Positive Predictive Value (PPV) and Negative Predictive Value (NPV), respectively. PPV and NPV represent the percentage of TP and TN among all data samples of two classes, respectively. Here, PPV and NPV represent the fraction of arteries and veins, correctly classi¯ed among all artery and vein samples, respectively, in data.
The highest vessel classi¯cation accuracy is observed for INSPIRE-AVR dataset with 93.9% correct rate using Relief-F ranking and proposed hybrid classi¯cation method. An interesting observation is the error rate for classi¯cation of artery samples in local dataset, with 6.2% and 5.3% mis-classi¯cation that is highest among all datasets. An obvious explanation for this result is the presence of pathological structures in local dataset images that deteriorate the appearance of arteries and thus make their classi¯cation more challenging. On the other hand, both for INSPIRE-AVR and VICAVR dataset, the misclassi¯cation rate for veins is more high as compared to arteries. Figure 22 shows an example of two fundus images, selected from local database (Fig. 22(a)) with Table 4. Optimal feature sets obtained via fusion of features using PCC (F P ) and Relief-F (F R ) ranking.

Comparison of vessel classi¯cation accuracy with other state-of-art approaches
The classi¯cation results presented for both healthy image database and diseased image database prove the capability of system in recognizing the vessels with higher accuracy.

AVR computation results
For evaluation purpose, the values of AVR calculated using the proposed method on three databases is compared with the corresponding AVR values in groundtruth. For INSPIRE-AVR database, we use the AVR values provided by both the observers 1 and 2 as benchmark for comparison and error calculation, since AVR estimated by an individual observer is dependent on his visual perception. We have used three parameters to assess the validity of our method in calculating AVR: (a) mean of di®erence between AVR values calculated by our system and those estimated by human expert, (b) mean of ratio of AVRs calculated automatically by our method to that of estimated manually, (c) mean of di®erence between AVRs by automatic method and average of (AVRs by observer 1 and 2). The parameter (a) is calculated by taking the mean of di®erence between AVRs generated by automatic system with the manual estimations. Parameter (b) is calculated by taking the ratio of AVRs calculated automatically to the corresponding AVRs given by human observer and then taking the mean of all those ratios. The closeness of parameter (b) which is basically mean of ratios with 1 depicts the closeness of AVRs automatically calculated and manually estimated. Parameter (c) is only calculated for INSPIRE-AVR  dataset. The use of these parameters has been motivated by Niemeijer et al., 33 and Dashtbozorg, Mendonça, Campilho, 38 who evaluated their AVR calculation methods using parameter (a), while the parameter (b) has been used by Ruggeri et al. 88 in order to analyze the closeness of AVRs obtained automatically with those estimated manually. Parameter (c) is proposed here in order to analyze the di®erence in AVR values by proposed method with the average of AVRs by two experts. By taking the di®erence with average of AVRs estimated by two di®erent observers, the bias towards the AVR values estimated by one person can be reduced. In order to carry out the comparative analysis, two parameters, i.e., (a) and (b), are also calculated for AVRs estimated by observer 1 and 2 for INSPIRE-AVR database to obtain inter-observer variability. This will allow to analyze the closeness of error between (automatic and manual AVRs) and (AVRs estimated by observer 1 and 2). Table 8 shows the performance of our system in AVR calculation and comparison with manual estimations for INSPIRE-AVR database. Note that there is considerable inter-observer di®erence in AVRs estimated by two observers. The AVR values calculated by our method are relatively closer to the AVRs estimated by observer 1 as compared to the AVRs estimated by observer 2. It is also important to mention that our method achieved mean error of 0.0565, that is close to the inter-observer error, i.e., 0.0520. When the mean of di®erence between automatically calculated AVRs and average of AVRs is taken, the mean error declines to 0.0477. Table 9 shows the results of AVR calculation for local and VICAVR databases, where the mean error is 0.0650 and 0.0849, respectively, larger than that calculated for INSPIRE-AVR database. Since the CAD systems are employed for acquiring diagnostic assessment, the presented results in Tables 8 and 9 demonstrate that the AVRs computed by our system can be considered as second independent opinion obtained from an automatic \Machine Expert". Furthermore, from the results of AVRs calculation on pathologically diseased database, it is revealed that our method is appreciable in providing the suitable AVR approximations.  Mean of ratios of AVRs estimated (by observer 1 to AVRs by observer 2) 1.0099 (c) Mean of di®erence of average of AVRs (estimated by observer 1 and 2) and AVRs by automatic method 0.0477 Although our method showed slight improvement in reducing mean error between AVRs automatically calculated and estimated by observer 1 than the ones given in Ref. 33, even then our method is still appreciable. As shown in Table 10, 89 evaluated their method using INSPIRE-AVR dataset by considering AVR annotations only by observer 1. When compared with the results proposed by Dashtbozorg et al. 89 on INSPIRE-AVR database, our method showed approximately similar mean error. The third comparison is made with the method by Mendonça et al., 40 in which automatic as well as semi-automated methods are used for AVR calculation and results are evaluated using the AVRs estimated by observer 1. Our method showed considerable superiority in calculating AVR values as compared to the AVRs calculated by Mendonça et al., 40 using automatic method. The comparison results in Table 10 show that our method surpasses the results reported by Niemeijer et al. 33 and Mendonça et al., 40 and presented similar mean error when compared to the AVR results reported by Dashtbozorg et al. 89

Discussion and Conclusion
The proposed methodology includes seven modules: (a) Automatic detection and segmentation of retinal vessels; (b) Extraction of novel feature set to categorize vessels; (c) Ranking of features by Pearson Correlation Coe±cient and Relief-F method; (d) Selection of features from ranked feature lists based on classi¯cation accuracy of three classi¯ers; (e) Classi¯cation of vessels by hybrid classi¯cation framework using selected feature subset; (f) Calculation of width of vessels and (g) Calculation of Arteriovenous Ratio. Particularly, two feature ranking techniques (PCC and Relief-F) followed by three classi¯ers for selection of features with multi-decision combination method for retinal vessel classi¯cation and subsequent AVR calculation, are evaluated in this paper for an improved HR detection system. The e®ect of speci¯c feature ranking techniques with the use of multiple classiers for feature selection and incorporation of \joint strength" of three supervised prediction models has not been evaluated in the past, therefore, the results obtained by the experiments can be used as a baseline or reference for future research.
The proposed methodology o®ers comparable results and works robustly on three databases acquired from di®erent fundus cameras with di®erent settings. The experimental evaluations highlight the strength of proposed vessel recognition model in capturing the relation between input features and classi¯cation outcomes e®ectively. Particularly, the arrangement of features and combinations of subsets according to feature lists ranked by PCC and Relief-F method have contributed to increase the retinal vessel classi¯cation accuracy, as compared to performance of features without ranking. The AVR computed using the proposed method agrees with the manually estimated AVR with an error of 0.0650, 0.0565 and 0.0849 for local database, INSPIRE-AVR and VICAVR database, respectively. Agreement observed in the experiment results for INSPIRE-AVR database is comparable to the inter-observer variability where the di®erence between AVR estimations of two experts is 0.0520. This di®erence exists due to visual perception discrimination present in the observers. It can be seen from Table 9 that the algorithm detects the subjects su®ering from HR with less error using images of low resolution and containing multiple retinal pathologies. It is successfully demonstrated that generalized arteriolar narrowing in retinal images can be quanti¯ed using the presented computer-aided process which may o®er an opportunity for reduction of disease progression The experimental results show AVR as a signi¯cant indicator for prediction of HR in an individual. The system does not require any complex computation; however, one of the important limitations of the proposed algorithm is its dependency on the vessel segmentation results.
Retinal vessels are known to be deteriorated in higher grades of HR which a®ects the vessel delineation process. Therefore, enhancing the performance of vessel segmentation is likely to improve the classi¯cation process, providing more e±cient and robust computer-aided analysis system. Another constraint of our method is the limit in vessel classi¯cation performance due to presence of retinal pathologies since these pathologies may in-°u ence re°ectivity. Although the presence of retinal pathologies is viewed to be less problematic in our research, the vessel classi¯cation and AVR measurement error remained high for images with the pathological structures. The segmentation of these pathologies from retinal images can contribute to the vessel classi¯cation e®ectiveness. Moreover, the sample size in our proposed research is comparatively small, especially for higher grades of HR. The experimental evaluations are promising; however, in this research we have not used all types of features for vessel classi¯cation and it requires more independent testing for validation of the fused classi¯cation scheme. Meanwhile, deep learning technology can be the way to achieve accurate vessel segmentation, which will form our future research. The structural information of vessels may allow acquiring better classi¯cation accuracy.